Question

In the Haber process for the production of ammonia, $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$ what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?

Short answer

The relationship between the rate of production of ammonia and the rate of consumption of hydrogen in the Haber process is \(\frac{\Delta[H_2]}{\Delta t}=-3\frac{\Delta[NH_3]}{2\Delta t}\).

Step-by-step solution

Write down the balanced chemical equation.

Write down the balanced chemical equation for the Haber process: \(N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g)\)

Analyze the stoichiometry of the reaction.

In the balanced chemical equation, the stoichiometric coefficients tell us the ratio in which the reactants are consumed and the products are formed. From the equation, we can see that 1 mole of nitrogen (N₂) reacts with 3 moles of hydrogen (H₂) to produce 2 moles of ammonia (NH₃).

Express the rate of production and consumption in terms of moles.

To express the relationship between the rates of production and consumption in terms of moles, we will call the rate of consumption of hydrogen (-Δ[H₂]/Δt) and the rate of production of ammonia (Δ[NH₃]/Δt). The stoichiometry of the equation tells us that for each mole of N₂ reacting, 3 moles of H₂ are consumed, and 2 moles of NH₃ are formed.

Find the relationship between the rates of production and consumption.

Using the stoichiometry of the reaction, we can now find the relationship between the rates of production and consumption of H₂ and NH₃. Since 3 moles of H₂ are consumed for every 2 moles of NH₃ produced, we can write the relationship as: \(-\frac{\Delta[H_2]}{3}=\frac{\Delta[NH_3]}{2}\) Next, we solve for the rate of consumption of hydrogen: \(\frac{\Delta[H_2]}{\Delta t}=-3\frac{\Delta[NH_3]}{2\Delta t}\) Therefore, the relationship between the rate of production of ammonia and the rate of consumption of hydrogen in the Haber process is: \(\frac{\Delta[H_2]}{\Delta t}=-3\frac{\Delta[NH_3]}{2\Delta t}\)

Key concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates of chemical reactions. It indicates how quickly or slowly a reaction proceeds. In the Haber process, measuring how fast ammonia is produced or how fast hydrogen is consumed allows us to understand the kinetics of the reaction.
To do this, we express these changes with reaction rates. Reaction rates are typically expressed as changes in concentration over time. For example, the rate at which ammonia ( NH_3) is formed is represented by the change in concentration of ammonia over a particular time period, noted as \(\frac{\Delta[NH_3]}{\Delta t}\). Similarly, the rate of hydrogen consumption is represented as \(\frac{\Delta[H_2]}{\Delta t}\).
The key to understanding kinetics in the context of the Haber process is the stoichiometry, as it dictates the relationship between the rates of consumption of reactants and the formation of the product.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is crucial in linking the rate of consumption of reactants with the rate of production of products, as it defines the proportions in a chemical reaction.
In the balanced equation for the Haber process, \(N_2(g) + 3H_2(g) \longrightarrow 2NH_3(g)\), the stoichiometric coefficients (numbers before each compound) reveal important information:

• 1 mole of nitrogen gas \(N_2\) is required.
• 3 moles of hydrogen gas \(H_2\) are consumed.
• 2 moles of ammonia \(NH_3\) are produced.

The stoichiometry gives us the ratios that relate the rate of consumption of hydrogen to the rate of production of ammonia. For every 3 moles of \(H_2\) consumed, 2 moles of \(NH_3\) are formed. This relationship helps us to establish the equation for reaction rates.

Ammonia Production

Ammonia production is a vital industrial process, prominently achieved by the Haber process. The synthesis of ammonia involves combining nitrogen and hydrogen under specific conditions of temperature and pressure. This single-stage reaction is critical for producing fertilizers essential in agriculture.
The efficiency of ammonia production hinges on the catalyst and conditions of the reaction. A catalyst, like iron, is used to increase the reaction rate without being consumed itself. It lowers the activation energy required for the reaction, thus accelerating the production process.
This industrial process is not only important for its role in agriculture but also impacts global food supply and various industrial applications. Ammonia is also a precursor for many products, including plastics, explosives, and textiles, highlighting its significance beyond just fertilizers.